32 ND I NTERNATIONAL C OSMIC R AY C ONFERENCE , B EIJING 2011

Estimation of 3D structures of cosmic-ray low density region behind shock waves associatedwith solar ﬂares
H. KOJIMA1 , S. S HIBATA2 , A. O SHIMA 3 , H. TAKAMARU2 , H. M. A NTIA4 , S. R. D UGAD4 , T. F UJII5 , S. K. G UPTA4 ,Y. H AYASHI5 , N. I TO5 , A. I YER4 , P. JAGADEESAN4 , A. JAIN4 , S. K AWAKAMI5 , K. K URAMOTO5 , D. M ATSUMIYA5 ,T. M ATSUYAMA 5 , M. M INAMINO5 , P. K. M OHANTY 4 , I. M ORISHITA6 , S. D. M ORRIS4 , P. K. NAYAK4 ,T. N ONAKA7 , S. O GIO5 , T. O KUDA5 , B. S. R AO4 , K. C. R AVINDRAN4 , K. S IVAPRASAD4 , P. S UBRAMANIAN4 ,H. TANAKA5 , S. C. T ONWAR4 , Y. YAMASHITA5 , K. YAMAZAKI51Faculty of Engineering, Aichi Institute of Technology, Toyota, Aichi, 470-0392, Japan
2College of Engineering, Chubu University, Kasugai, Aichi, 487-8051, Japan
3National Astronomical Observatory of Japan, Mitaka, Tokyo, 181-8588, Japan
4
Tata Institute of Fundamental Research, Homi Bhabha Road, Munbai, 400005, India
5
Graduate School of Science, Osaka City University, Sumiyoshi, Osaka, 558-8585, Japan
6
Department of Information Management, Asahi University, Hozumi, Gifu, 501-0296, Japan
7
Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba, 277-8582,Japan
shibata@isc.chubu.ac.jp
DOI: 10.7529/ICRC2011/V10/0983
Abstract: Using the data obtained by GRAPES-3 tracking muon telescope at Ooty, we are going to estimate the 3D
structure of low density cosmic ray region caused by large solar ﬂares. Since the GRAPES-3 muon telescope has a large
acceptance (∼ 3 sr) with ﬁne segmentation (13×13), hourly 2D maps of multi-directional cosmic-ray intensity variations
are easily obtained by this telescope. By comparing the time sequence of these 2D maps with the results of computer
simulations in which some models of structure of the low density cosmic-ray region behind shock waves are assumed,
we will try to extract their 3D structure of the region. In this paper, we examine the time proﬁles of the Forbush decreases
so far observed and compare them with the time proﬁles of the solar wind velocity. Then, we present a simple 3D shock
wave propagation model and draw a sample contour map of cosmic ray intensity for getting the idea about what we will
be able to deduce from 2D maps of GRAPES-3 by comparison.
Keywords: Solar ﬂare, Cosmic-ray low density region, 3D structure, GRAPES-3 tracking muon telescope

1Introduction

It is thought that the transient phenomena of cosmic-ray
intensity variations such as Forbush decreases and/or thecosmic-ray local (small scale) anisotropies are caused byshock waves (i.e. some unusual or special structures of theinterplanetary magnetic ﬁeld) associated with Solar ﬂares,
coronal mass ejections or high speed ﬂows of the solar
wind, because cosmic rays near the area may be brownaway by such shock waves and some low density region
might be made. So it is expected that the observation andanalysis of cosmic-ray intensity variations will provide important information about the 3D structure of such low density region caused by the shock wave.
So far, this kind of phenomena have been mainly investigated by using muon or neutron monitors those have relatively less angular resolutions [1] [2]. In order to observe
the more ﬁne structure of the low density region caused by
the shock wave, the more angular resolution with multidirectional ﬁeld of view is required. The GRAPES-3 track-ing muon telescope is the one of such detectors suitable tostudy transient phenomena or local anisotropies of the cosmic rays [3] [4] [5] [6] [7] [8]. The ﬁeld of view of thetelescope is schematically shown in Fig.1.
The GRAPES-3 tracking muon telescope is located atOoty, India (11.4◦ N, 76.7◦ E). It consists of 16 modules of35 m2 muon detectors, and the acceptance is about ∼ 3 sr.
This telescope can record the hourly 2D map of the arrival
direction of muons above 1 GeV with 13 × 13 ﬁne segmentation. The detailed explanation of the detector can befound elsewhere [3] [4] [5] [6] [7].

2 Time proﬁle of the Forbush decrease
Before showing an example 2D map of the Forbush decrease viewed by the GRAPES-3 tracking muon telescope,
we present several examples of the time proﬁles of Forbush decreases comparing with the time proﬁles of the solar wind velocity, here.

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Figure 2: An example of Forbush Decrease observed behind the increase of the solar wind velocity.
Figure 1: The ﬁeld of view of the GRAPES-3 tracking
muon telescope.
In all Figs.2 – 6, the daily averaged solar wind velocity andthe daily averaged cosmic ray intensities of NW, N, NE, W,V, E, SW, S, SE components, which are corresponding directions to the letters indicated in Fig.1, are shown. For all
the ﬁgures, the abscissa indicates the day of the observation, the left ordinate indicates the variation of cosmic rayintensities in %, and the right ordinate indicates the variation of solar wind velocity in km/s.
In case of Figs.2 and 3, peaks of the solar wind velocity precede valleys of the cosmic ray intensity, on the other hand,in case of Figs.4 and 5, the order is reversed. There areother examples in which a peak of the solar wind velocity
and a valley of the cosmic ray intensity observed simultaneously at the Earth, as shown in Fig.6. Of course, there
also exist more complicated events. The relation between
the time proﬁle of the variation of cosmic ray intensities
and that of solar wind velocities is differ from one event toanother.

3

Figure 3: An example of Forbush Decrease observed behind the increase of the solar wind velocity.

Figure 4: An example of Forbush Decrease precedes theincrease of the solar wind velocity.

Simple model calculation

From the data of only one dimensional time sequences, it
is not easy to deduce the complicated relations as seen in
the examples of the previous section. So, we are goingto use hourly 2D maps of multi-directional cosmic-ray intensity variations provided by GRAPES-3 tracking muon
telescope.
Here, we introduce a simple 3D shock wave propagation
model as a tool to make correspondences between 3D structures of low density cosmic ray region and 2D maps of cosmic ray intensity. Schematic view of the model is shown inFig.7. In this model, it is assumed that a shock front of theinterplanetary magnetic ﬁeld is a simple plane and propagate a given direction strait with a constant speed (e.g.
∼ 600 km/s). For the calculation of cosmic ray intensities, at this time, we assumed that cosmic rays behind theshock front is totally swept out and the intensity of cosmic rays is proportional to the distance from the Earth tothe boundary which is determined by the shock front andthe spherical shell centered at the Earth with a given radiusFigure 5: An example of Forbush Decrease precedes theincrease of the solar wind velocity.

Figure 6: An example of Forbush Decrease observed simultaneously to the increase of the solar wind velocity.

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32 ND I NTERNATIONAL C OSMIC R AY C ONFERENCE , B EIJING 2011

Though the result presented here is only limited to the qualitative comparison, this is the ﬁrst trial and there is the potential to develop a useful tool to estimate the 3D structure of low density cosmic ray region caused by large solar
ﬂares.

Acknowledgements

Figure 7: A simple 3D shock wave propagation model foran estimation of cosmic ray intensity 2D maps.

The authors express our thanks to the staff of the neutron
monitor station at Kiel for providing the cosmic ray data used in this analysis. The staffs of Space Physics Data
Facility (SPDF) and National Space Science Data Center(NSSDC) are also acknowledged for allowing us to use thedata in OMNI 2 data set.
This work is partly supported by the grant in aid of theSolar Terrestrial Environment Laboratory of Nagoya University and the Institute for Cosmic Ray Research of University of Tokyo.

References

Figure 8: A Forbush decrease observed by the GRAPES-3
tracking muon telescope (V, W, E) and the time proﬁle ofsolar wind velocity around 15 (from 12 to 21), Dec., 2006.
(e.g. 0.25 AU). The orientation of the (multi-directional)
telescope and the rotation of the Earth are, of course, also
taken into account.
As a typical example, observed 2D maps of cosmic-ray intensity variations correspond to Forbush decrease observed
around 15, Dec., 2006 (the hourly averaged solar wind velocity and that of cosmic ray intensities are shown in Fig.8)
and the calculated contour maps are compared in Fig.9.
From this ﬁgure, very clear qualitative correspondences areseen between the calculation and the observation.

4Conclusion

From the comparison of the time proﬁles of the Forbush
decreases with those of solar wind velocities, we can conclude that the relation between them are differ from one
event to another, and it is not easy to deduce the complicated relations from the data of only one dimensional time
sequences, at ﬁrst.
Next, introducing the simple 3D shock wave propagation
model and drawing the sample contour map of cosmic rayintensity help us to examine the relation between physical(or plasma) and geometrical parameters of the solar wind(or the 3D structure of low density cosmic ray region) andthe hourly 2D maps provided by GRAPES-3.

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Figure 9: Calculated and observed Forbush decrease viewed by the GRAPES-3 tracking muon telescope around 15 (from7 to 17), Dec., 2006.

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